I came across an interesting section in Albert H.
Beiler's Recreations in the Theory of Numbers,
Second Edition, Dower Publications Inc, page 222. He
talks about Palindromic primes in AP. I was able to
generate palindromic primes in AP with lengths 3 and
4.

For puzzle 759 there is already some great work done on this in
Patrick DeGeest's fine
website at http://www.worldofnumbers.com/palprim2.htm#warut. Just
scroll down to
almost the bottom of the page and look for the heading 'Smallest
Palprimes in 'Arithmetic Progression'
by Warut Roonguthai [ June 21-24, 1999 ]

There are many pairs (p,d) that generates
palindromic primes in AP of length 5 and 6. In fact there are many
sets of consecutive Palindromic Primes in AP of length 5 and 6.
For example :
(1) Initial terms of smallest sets of consecutive palindromic primes
in AP of length 5 are given by Sloanes OEIS A059122 as follows: